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Geometrodynamical Analysis to Characterize the Dynamics and Stability of a Molecular System through the Boundary of the Hill’s Region

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DOI: 10.4236/am.2014.516251    3,470 Downloads   3,852 Views  

ABSTRACT

In this paper we study the dynamics and stability of a two-dimensional model for the vibrations of the LiCN molecule making use of the Riemannian geometry via the Jacobi-Levi-Civita equations applied to the Jacobi metric. The Stability Geometrical Indicator for short times is calculated to locate regular and chaotic trajectories as the relative extrema of this indicator. Only trajectories with initial conditions at the boundary of the Hill’s region are considered to characterize the dynamics of the system. The importance of the curvature of this boundary for the stability of trajectories bouncing on it is also discussed.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Vergel, A. , Benito, R. , Losada, J. and Borondo, F. (2014) Geometrodynamical Analysis to Characterize the Dynamics and Stability of a Molecular System through the Boundary of the Hill’s Region. Applied Mathematics, 5, 2630-2642. doi: 10.4236/am.2014.516251.

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